Definition:Usual Ordering of Ordinals

Definition

Let $\On$ denote the class of all ordinals.

The usual ordering $\le$ on $\On$ is the subset relation:

$a \le b \iff a \subseteq b$

and its corresponding strict version:

$a < b \iff a \subsetneqq b$

Also see

• Well-Ordering of Class of All Ordinals under Subset Relation, demonstrating that $\le$ is a well-ordering.

Sources

• 2010: Raymond M. Smullyan and Melvin Fitting: Set Theory and the Continuum Problem (revised ed.) ... (previous) ... (next): Chapter $5$: Ordinal Numbers: $\S 1$ Ordinal numbers